ਫੋਰੀਅਰ ਪਰਿਵਰਤਨ

ਇੱਕ ਸਾਈਨੁਸੋਆਇਡਲ ਵਕਰ, ਜਿਸਦਾ ਉੱਚਤਮ ਐਂਪਲੀਟਿਊਡ (1) ਹੈ।  ਫੇਜ਼ ਸ਼ਿਫਟ θ ਦਾ ਚਿੱਤ੍ਰਣ।

$\scriptstyle f(t)$

$\scriptstyle {\hat {f}}(\omega )$

$\scriptstyle g(t)$

$\scriptstyle {\hat {g}}(\omega )$

$\scriptstyle t$

$\scriptstyle \omega$

$\scriptstyle t$

$\scriptstyle \omega$

In the first row is the graph of the unit pulse function $f(t)$ and its Fourier transform ${\hat {f}}(\omega )$, a function of frequency $\omega$. Translation (that is, delay) in the time domain goes over to complex phase shifts in the frequency domain. In the second row is shown $g(t)$, a delayed unit pulse, beside the real and imaginary parts of the Fourier transform. The Fourier transform decomposes a function into eigenfunctions for the group of translations.

ਫੋਰੀਅਰ ਪਰਿਵਰਤਨ
ਨਿਰੰਤਰ ਫੋਰੀਅਰ ਪਰਿਵਰਤਨ
ਫੋਰੀਅਰ ਸੀਰੀਜ਼
ਅਨਿਰੰਤਰ-ਸਮਾਂ ਫੋਰੀਅਰ ਪਰਿਵਰਤਨ
ਅਨਿਰੰਤਰ ਫੋਰੀਅਰ ਪਰਿਵਰਤਨ
ਕਿਸੇ ਛੱਲੇ ਉੱਪਰ ਅਨਿਰੰਤਰ ਫੋਰੀਅਰ ਪਰਿਵਰਤਨ
ਫੋਰੀਅਰ ਵਿਸ਼ਲੇਸ਼ਣ
ਸਬੰਧਤ ਪਰਿਵਰਤਨ

ਫੋਰੀਅਰ ਪਰਿਵਰਤਨ ਵਕਤ ਦੇ ਕਿਸੇ ਫੰਕਸ਼ਨ (ਕਿਸੇ ਸਿਗਨਲ) ਨੂੰ ਅਜਿਹੀਆਂ ਫਰੀਕੁਐਂਸੀਆਂ ਵਿੱਚ ਤੋੜ ਦਿੰਦਾ ਹੈ ਜੋ ਇਸਨੂੰ ਉਸੇ ਤਰੀਕੇ ਨਸਾਲ ਬਣਾ ਦਿੰਦੀਆਂ ਹਨ, ਜਿਵੇਂ ਕੋਈ ਸੰਗੀਤਕ ਤਾਰ ਨੂੰ ਇਸਦੇ ਰਚਣਹਾਰੇ ਨੋਟਾਂ ਦੇ ਐਂਪਲੀਟਿਊਡ (ਜਾਂ ਉੱਚੇਪਣ) ਦੇ ਤੌਰ 'ਤੇ ਦਰਸਾਇਆ ਜਾ ਸਕਦਾ ਹੈ।

ਇਹ ਵੀ ਦੇਖੋ

• ਐਨਾਲੌਗ ਸੰਕੇਤ ਵਿਕਾਸ
• ਬੀਵਰਜ਼-ਲਿਪਸਨ ਸਟਰਿਪ
• ਅਨਿਰੰਤਰ ਫੋਰੀਅਰ ਪਰਿਵਰਤਨ
  • DFT ਮੈਟ੍ਰਿਕਸ
• ਅਨਿਰੰਤਰ-ਸਮਾਂ ਫੋਰੀਅਰ ਪਰਿਵਰਤਨ
• ਤੇਜ਼ ਫੋਰੀਅਰ ਪਰਿਵਰਤਨ
• ਫੋਰੀਅਰ ਇੰਟਗ੍ਰਲ ਓਪਰੇਟਰ
• ਫੋਰੀਅਰ ਇਨਵਰਸ਼ਨ ਥਿਓਰਮ
• ਫੋਰੀਅਰ ਮਲਟੀਪਲਾਇਰ
• ਫੋਰੀਅਰ ਸੀਰੀਜ਼
• ਫੋਰੀਅਰ ਸਾਈਨ ਪਰਿਵਰਤਨ
• ਫੋਰੀਅਰ-ਡੈਲੀਗਨੇ ਪਰਿਵਰਤਨ
• ਫੋਰੀਅਰ-ਮੁਕਾਇ ਪਰਿਵਰਤਨ
• ਭਿੰਨਾਤਮਿਕ ਫੋਰੀਅਰ ਪਰਿਵਰਤਨ
• ਅਸਿੱਧਾ ਫੋਰੀਅਰ ਪਰਿਵਰਤਨ
• ਇੰਟਗ੍ਰਲ ਪਰਿਵਰਤਨ
  • ਹੈਂਕਲ ਪਰਿਵਰਤਨ
  • ਹਾਰਟਲੇ ਪਰਿਵਰਤਨ
• ਲਾਪਲੇਸ ਪਰਿਵਰਤਨ
• ਰੇਖਿਕ ਕਾਨੋਨੀਕਲ ਪਰਿਵਰਤਨ
• ਮਿਲਿੱਨ ਪਰਿਵਰਤਨ
• ਬਹੁਅਯਾਮੀ ਪਰਿਵਰਤਨ
• NGC 4622, ਖਾਸਤੌਰ 'ਤੇ ਤਸਵੀਰ NGC 4622 ਫੋਰੀਅਰ ਪਰਿਵਰਤਨ m = 2.
• ਅਲਪ-ਕਾਲੀਨ ਫੋਰੀਅਰ ਪਰਿਵਰਤਨ
• ਸਪੇਸ-ਟਾਈਮ ਫੋਰੀਅਰ ਪਰਿਵਰਤਨ
• ਸਪੈਕਟ੍ਰਲ ਘਣਤਾ
  • ਸਪੈਕਟ੍ਰਲ ਘਣਤਾ ਅਨੁਮਾਨ
• ਚਿੰਨਾਤਮਿਕ ਇੰਟੀਗ੍ਰੇਸ਼ਨ
• ਸਮਾਂ ਖਿੱਚ ਡਿਸਪਰਸਿਵ ਫੋਰੀਅਰ ਪਰਿਵਰਤਨ
• ਪਰਿਵਰਤਨ (ਗਣਿਤ)

ਹਵਾਲੇ

• Boashash, B., ed. (2003), Time-Frequency Signal Analysis and Processing: A Comprehensive Reference, Oxford: Elsevier Science, ISBN 0-08-044335-4 
• Bochner S., Chandrasekharan K. (1949), Fourier Transforms, Princeton University Press 
• Bracewell, R. N. (2000), The Fourier Transform and Its Applications (3rd ed.), Boston: McGraw-Hill, ISBN 0-07-116043-4 .
• Campbell, George; Foster, Ronald (1948), Fourier Integrals for Practical Applications, New York: D. Van Nostrand Company, Inc. .
• Condon, E. U. (1937), "Immersion of the Fourier transform in a continuous group of functional transformations", Proc. Natl. Acad. Sci. USA 23: 158–164 .
• Duoandikoetxea, Javier (2001), Fourier Analysis, American Mathematical Society, ISBN 0-8218-2172-5 .
• Dym, H; McKean, H (1985), Fourier Series and Integrals, Academic Press, ISBN 978-0-12-226451-1 .
• Erdélyi, Arthur, ed. (1954), Tables of Integral Transforms, 1, New Your: McGraw-Hill 
• Gerald Folland (1989), Harmonic analysis in phase space, Princeton University Press 
• Fourier, J. B. Joseph (1822), Théorie Analytique de la Chaleur, Paris: Chez Firmin Didot, père et fils, http://books.google.com/books?id=TDQJAAAAIAAJ&pg=PA525&dq=%22c%27est-%C3%A0-dire+qu%27on+a+l%27%C3%A9quation%22&hl=en&sa=X&ei=SrC7T9yKBorYiALVnc2oDg&sqi=2&ved=0CEAQ6AEwAg#v=onepage&q=%22c%27est-%C3%A0-dire%20qu%27on%20a%20l%27%C3%A9quation%22&f=false 
• Fourier, J. B. Joseph; Freeman, Alexander, translator (1878), The Analytical Theory of Heat, The University Press, http://books.google.com/books?id=-N8EAAAAYAAJ&pg=PA408&dq=%22that+is+to+say,+that+we+have+the+equation%22&hl=en&sa=X&ei=F667T-u5I4WeiALEwpHXDQ&ved=0CDgQ6AEwAA#v=onepage&q=%22that%20is%20to%20say%2C%20that%20we%20have%20the%20equation%22&f=false 
• Champeney, D.C. (1987), A Handbook of Fourier Theorems, Cambridge University Press 
• de Groot, Sybren R.; Mazur, Peter (1984), Non-Equilibrium Thermodynamics (2nd ed.), New York: Dover 
• Marín Antuña, José (1990), Teoría de funciones de variable compleja (2nd ed.), Havana: Editorial Pueblo y Educación 
• Chatfield, Chris (2004), The Analysis of Time Series: An Introduction, Texts in Statistical Science (6th ed.), London: Chapman & Hall/CRC 
• Feller, William (1971), An Introduction to Probability Theory and Its Applications. Vol. II. (Second ed.), New York: John Wiley & Sons .
• Wiener, Norbert (1949), Extrapolation, Interpolation, and Smoothing of Stationary Time Series With Engineering Applications, Cambridge, Mass.: Technology Press and John Wiley & Sons and Chapman & Hall 
• Kirillov, Alexandre; Gvichiani, Alexei (1982), Théorèmes et problèmes d'analyse fonctionnelle, Djilali Embarek, translator, Moscow: Mir 
• Kolmogórov, Andréi Nikolaevich; Fomín, Serguei Vasílievich (1978), Elementos de la teoría de funciones y del análisis functional, Carlos Vega, translator (3rd ed.), Moscow: Mir 
• Guelfand, Israel Moiseevich; Vilenkin, N.Y. (1967), Les distributions tome 4: applications de l'analyse harmonique, G. Rideau, translator, Paris: Dunod 
• Widder, David Vernon; Wiener, Norbert (August 1938), "Remarks on the Classical Inversion Formula for the Laplace Integral", Bulletin of the American Mathematical Society 44: 573–575, doi:10.1090/s0002-9904-1938-06812-7 
• Clozel, Laurent; Delorme, Patrice (1985), "Sur le théorème de Paley-Wiener invariant pour les groupes de Lie réductifs réels", C. R. Acad. Sci. Paris, série I 300: 331–333 
• Paley, R.E.A.C.; Wiener, Norbert (1934), Fourier Transforms in the Complex Domain, American Mathematical Society Colloquium Publications, Providence, Rhode Island: American Mathematical Society 
• Grafakos, Loukas (2004), Classical and Modern Fourier Analysis, Prentice-Hall, ISBN 0-13-035399-X .
• Grafakos, Loukas; Teschl, Gerald (2013), "On Fourier transforms of radial functions and distributions", J. Fourier Anal. Appl. 19: 167–179, doi:10.1007/s00041-012-9242-5 .
• Greiner, W.; Reinhardt, J. (1996), Field Quantization, Springer Publishing, ISBN 3-540-59179-6 
• Hewitt, Edwin; Ross, Kenneth A. (1970), Abstract harmonic analysis. Vol. II: Structure and analysis for compact groups. Analysis on locally compact Abelian groups, Die Grundlehren der mathematischen Wissenschaften, Band 152, Berlin, New York: Springer-Verlag .
• Hörmander, L. (1976), Linear Partial Differential Operators, Volume 1, Springer-Verlag, ISBN 978-3-540-00662-6 .
• James, J.F. (2011), A Student's Guide to Fourier Transforms (3rd ed.), New York: Cambridge University Press, ISBN 978-0-521-17683-5 .
• Kaiser, Gerald (1994), A Friendly Guide to Wavelets, Birkhäuser, ISBN 0-8176-3711-7, http://books.google.com/books?id=rfRnrhJwoloC&pg=PA29&dq=%22becomes+the+Fourier+%28integral%29+transform%22&hl=en&sa=X&ei=osO7T7eFOqqliQK3goXoDQ&ved=0CDQQ6AEwAA#v=onepage&q=%22becomes%20the%20Fourier%20%28integral%29%20transform%22&f=false 
• Kammler, David (2000), A First Course in Fourier Analysis, Prentice Hall, ISBN 0-13-578782-3 
• Katznelson, Yitzhak (1976), An introduction to Harmonic Analysis, Dover, ISBN 0-486-63331-4 
• Knapp, Anthony W. (2001), Representation Theory of Semisimple Groups: An Overview Based on Examples, Princeton University Press, ISBN 978-0-691-09089-4, http://books.google.com/?id=QCcW1h835pwC 
• Müller, Meinard (2015), The Fourier Transform in a Nutshell., In Fundamentals of Music Processing, Section 2.1, pages 40-56: Springer, doi:10.1007/978-3-319-21945-5, ISBN 978-3-319-21944-8, https://www.audiolabs-erlangen.de/content/05-fau/professor/00-mueller/04-bookFMP/2015_Mueller_FundamentalsMusicProcessing_Springer_Section2-1_SamplePages.pdf 
• Pinsky, Mark (2002), Introduction to Fourier Analysis and Wavelets, Brooks/Cole, ISBN 0-534-37660-6, http://books.google.com/books?id=tlLE4KUkk1gC&pg=PA256&dq=%22The+Fourier+transform+of+the+measure%22&hl=en&sa=X&ei=w8e7T43XJsiPiAKZztnRDQ&ved=0CEUQ6AEwAg#v=onepage&q=%22The%20Fourier%20transform%20of%20the%20measure%22&f=false 
• Polyanin, A. D.; Manzhirov, A. V. (1998), Handbook of Integral Equations, Boca Raton: CRC Press, ISBN 0-8493-2876-4 .
• Rudin, Walter (1987), Real and Complex Analysis (Third ed.), Singapore: McGraw Hill, ISBN 0-07-100276-6 .
• Rahman, Matiur (2011), Applications of Fourier Transforms to Generalized Functions, WIT Press, ISBN 1845645642, http://books.google.com/books?id=k_rdcKaUdr4C&pg=PA10 .
• Stein, Elias; Shakarchi, Rami (2003), Fourier Analysis: An introduction, Princeton University Press, ISBN 0-691-11384-X, http://books.google.com/books?id=FAOc24bTfGkC&pg=PA158&dq=%22The+mathematical+thrust+of+the+principle%22&hl=en&sa=X&ei=Esa7T5PZIsqriQKluNjPDQ&ved=0CDQQ6AEwAA#v=onepage&q=%22The%20mathematical%20thrust%20of%20the%20principle%22&f=false .
• Stein, Elias; Weiss, Guido (1971), Introduction to Fourier Analysis on Euclidean Spaces, Princeton, N.J.: Princeton University Press, ISBN 978-0-691-08078-9, http://books.google.com/books?id=YUCV678MNAIC&dq=editions:xbArf-TFDSEC&source=gbs_navlinks_s .
• Taneja, HC (2008), "Chapter 18: Fourier integrals and Fourier transforms", Advanced Engineering Mathematics:, Volume 2, New Delhi, India: I. K. International Pvt Ltd, ISBN 8189866567, http://books.google.com/books?id=X-RFRHxMzvYC&pg=PA192&dq=%22The+Fourier+integral+can+be+regarded+as+an+extension+of+the+concept+of+Fourier+series%22&hl=en&sa=X&ei=D4rDT_vdCueQiAKF6PWeCA&ved=0CDQQ6AEwAA#v=onepage&q=%22The%20Fourier%20integral%20can%20be%20regarded%20as%20an%20extension%20of%20the%20concept%20of%20Fourier%20series%22&f=false .
• Titchmarsh, E (1948), Introduction to the theory of Fourier integrals (2nd ed.), Oxford University: Clarendon Press (published 1986), ISBN 978-0-8284-0324-5 .
• Vretblad, Anders (2000), Fourier Analysis and its Applications, Graduate Texts in Mathematics, 223, New York: Springer Publishing, ISBN 0-387-00836-5 
• Wilson, R. G. (1995), Fourier Series and Optical Transform Techniques in Contemporary Optics, New York: Wiley, ISBN 0-471-30357-7 .
• Yosida, K. (1968), Functional Analysis, Springer-Verlag, ISBN 3-540-58654-7 .

ਬਾਹਰੀ ਲਿੰਕ

• Weisstein, Eric W., "ਫੋਰੀਅਰ ਪਰਿਵਰਤਨ" from MathWorld.